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t0EC44USN
Fourth Semester B.E. Degree Examination, Dec.2013 lJan.2ol4Signals and Systems
Time: 3 hrs.
Ia.
Note: Answer FIVEfull questions, selectingat least TWO questions from esch port.
PART _ ASketch the even and odd part of the signal shown in Fig.Ql(a).
Max. Marks:100,],
. '!'':;",, ,:', ""'
(06 Marks)
(06 Marks)(08 Marks)
(04 Marks)
(06 Marks)
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.= 6l
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'..'.,., Fig.Ql(a)b. Check whether the following signals is periodic or not'and if periodic find its fundamental
period.(i) x(n): cos(2Onn) + sin(50nn) (ii) x(t) = [cos(2nt)]2
c. Let x(t) and y(t) as shown in Fig.Ql(c). Sketch (i) x(t)y(t - 1) (ii) x(t)y(-t -1)
Y(r)
t
2a.
b.
3a.
b.
Fig.Q1(c)Determine the convolution sum of the given sequences
x(n) = {1; -2,3, -3} and h(n) = {-2,2,-2\' ,l\,lrlll
Performthe convolution of the following sequences:
" xl(t):e-at ; 0<t<T,,,:::::::
:,," xz(t):1 ; 0<t<27:..::
G. ,q.n LTl system is characterized by an impulse response,
response of the system for the input x(n; = [1]'r,rr.t4t\,./
Find the natural response of the system described by a differential equation
d2y(t) "
dy(t)dr, *. d, + 2y(t) =2x(t). with y(0) : l. and #1,=, = o
(10 Marks)
/r\nh1n;=l- l ,(n). Find the
|') I\L /
Determine the following LT1 systems characterued by impulse reponse is memory, causal
and stable.(i) h(n) : 2u(n) - 2u(n-2) (ii) h(n) : (0.99)'u(n + 6). (06 Marks)
1 of2
(06 Marks)
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t0EC44c. Find the difference equation description for the system shown in Fig.Q3(c). (04 Marks)
Fie.Q3(c)d. By converting the differential equation to integral equation draw the direct form-I and direct
Y ("1
form-Il implementation for the system as
qJ$* a
d'y(t) * 1 dy(t) = x(t) * u
d2x(t)
dtr .*
dt' -t
d, -n\t/ I v dt2
"...., PART_B .
a. Find the DTFT of the following signals:
(04 Marks)
4a.
b.
State and prove the following properties of DTFS: (i) Modulation (ir) Parseval's,ni,%riil;u.,
Find theFourier series coefficients of the signal x(t) shown in Fig.Q4(b) and also draw itsspectra. (10 Marks)
-Tr flFie.Qs(b)
(i) x(n):unl' lal<1 (iil x(n) :2'u(-n) (08 Marks)(06 Marks)
(06 Marks)
b. Determine the signal x(n) if its DTFT is as shown in Fig.Q5(b).c. Compute the Fourier transform of the signal
fl+cosnt : lti<lx(t) = 1|. 0 : ltl>la. Find the frequency respanse of the system described by the impulse response
h(t) : a(r) - 2e 2t i(t)and also draw its magnitude and phase spectra.
b. Obtain the Fourier translorm representation for the periodic signalx(t) : sin wot
and draw the magnitude and phase.
c. A signal'x(t): cos(20nt) + % cos(30nt) is sampled with sampling periodNyqaisf rate.
a. ffiat is region of convergence (ROC)? Mention its properties.b: ' Determine the z-transform and ROC of the sequence x(n) = riu(n) + riu(-n).
l+z-'C. Determine the inverse z-transform of the function, x(z) = l-z-t +0.52-2 'fraction expanslon.
8 a. An LT1 system is described by the equationy(n): x(n) + 0.8 x(n- 1) + 0.8x(n -2) -0.49y(n-2)
b. Determine the transfer function H(z) of the system and also sketch the poles and zeros.(06 Marks)
c. Determine whether the system described by the equationy(n):x(n) + by(n- 1) is causal and stablewhere lb l< 1. (08Marks)
Find the unilateral z-transform for the sequence y(n) : x(n - 2), where x(n) : o'. (06 Marks)-r-:;-
(08 Marks)
(07 Marks)
tr. Find the(05 Marks)
(06 Marks)
, (07 Marks)
using partial
(07 Marks)
Fig.QaG)
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